Growth of ocean thermal energy conversion resources under greenhouse warming regulated by oceanic eddies

The concept of utilizing a large temperature difference (>20 °C) between the surface and deep seawater to generate electricity, known as the ocean thermal energy conversion (OTEC), provides a renewable solution to fueling our future. However, it remains poorly assessed how the OTEC resources will respond to future climate change. Here, we find that the global OTEC power potential is projected to increase by 46% around the end of this century under a high carbon emission scenario, compared to its present-day level. The augmented OTEC power potential due to the rising sea surface temperature is partially offset by the deep ocean warming. The offsetting effect is more evident in the Atlantic Ocean than Pacific and Indian Oceans. This is mainly attributed to the weakening of mesoscale eddy-induced upward heat transport, suggesting an important role of mesoscale eddies in regulating the response of thermal stratification and OTEC power potential to greenhouse warming.

temperatures do not vary a lot with seasons. Large temperature differences mentioned in the abstract is also not very informative since OTEC operates on temperature differences of ~ 20°C. 2. It would be interesting to see in the introduction some specific global warming mechanisms that target changes in ocean water temperatures, and by how much ocean water has changed over the years. Trends in changes of ocean surface and deep water temperatures over the years would be useful -higher rate of change in temperatures is projected in Extended Fig. 1. The high carbon emission scenario leading to temperature changes of ocean water discussed in the paper can also be quantified. 3. It is easier to comprehend the influence of global warming on surface ocean water. Deep cold water used by OTEC plants is ~1000 m below the ocean surface and the surface atmospheric effects would be almost negligible. Also, there is a lack in natural mixing between surface warm water and deep cold water. Hence, it is not easy to follow how DOW would be directly impacted by global warming. More discussions are required, particularly on the influence of ocean currents which is a focus of this paper. DOW temperatures remain almost constant (4 -6 °C) at 1000 m throughout the world, while surface temperatures vary with region. Therefore, some form of evidence is necessary that the DOW does change with global warming. 4. The different regions (Pacific, Atlantic, etc) can be labelled on the contour maps for better clarity in result presentation. 5. It is difficult to link some of the discussions in the paper with the figures. This should be improved throughout the paper.  Table 1 is not clear. 6. The geographical differences between China and Mexico affects the OTEC power due to differences in vertical ocean thermal gradients. As mentioned above, reasons for such regional differences in thermal gradients and OTEC power should be well explained. 7. As acknowledged, the OTEC power depends on the thermal gradient with depth, regardless of the rates of changes in the surface and deep ocean water. Therefore, global warming may not always improve OTEC power, since the temperature gradient could change or remain same. This could be highlighted as a key outcome and could serve as a guide for potential future researchers investigating this topic. The growth of OTEC resource mentioned in the title may not be appropriate as well.

Reply to the first reviewer
We are very grateful to you for your time in carefully reading our manuscript and providing helpful comments that make our manuscript better. We have carefully considered each of your comments (in blue) and revised the manuscript accordingly.
Please find our response (in black) to your comments below.

Reviewer #1 (Remarks to the Author):
This paper addresses an issue that is extremely timely, that is whether the amount of energy that could be extracted from OTEC could potentially significantly decrease or increase in the future. They use a state of the art high resolution climate model in the analysis. The manuscript would be suitable for publication if it is significantly edited for clarity. In several places the authors overstate the differences between the results found with the high-resolution simulation and that found in CMIP6 with respect to the changes in OTEC potential in the future. It would be good to include the location of the EEZs on the one of the maps, for instance Figure 1. In addition, the authors should report the standard deviations and/or significance level for their calculations including those mentioned in my comments below.
Following your comments, we have revised the statements in the manuscript to avoid unclarity. Furthermore, we have provided the standard errors for the estimated quantities and provided details on how the standard errors are computed (See "Computation of standard errors" in Methods). Based on the standard errors, we demonstrate that the time-mean OTEC power potential in the coarse-resolution CMIP6 CGCM ensemble mean (7.21 ± 0.30 TW) is significantly smaller than those in the CESM-H (8.55 ± 0.11 TW) and observation (9.36 ± 0.04 TW). Although the linear trend of OTEC power potential in the coarse-resolution CMIP6 CGCM ensemble mean during 1955-2021 (2.08 ± 0.31 TW/century) is larger than those in the CESM-H (1.99 ± 0.59 TW/century) and observation (1.80 ± 0.22 TW/century), the differences of the trends between the coarse-resolution CMIP6 CGCM ensemble mean, CESM-H and observation are not statistically significant. Therefore, we have to admit that we overstate the difference in the simulated OTEC power potential between the CMIP6 CGCMs and CESM-H. In the revised manuscript, we have revised the statement as: "Based on the above comparisons, we conclude that the CESM-H generally provides a reliable simulation of OTEC power potential during 1955-2021. Specifically, it simulates a linear trend of OTEC power potential similar to those in the observation and CMIP6 CGCM ensemble mean but outperforms the CMIP6 CGCM ensemble mean in the simulated time-mean OTEC power potential. This lends support to using the CESM-H for projecting the future OTEC power potential change by the end of this century." (Line 134-139) Finally, we have shown the location of the EEZs across the globe in the revised 1. Line 17: I believe that the authors mean "power potential".
Revised. Please see Line 14.
2. Line 19: "the exclusive economic zone" needs to be modified for clarity. Maybe the authors mean the exclusive economic zones across the globe?
Thank you for your comment. This phrase has been deleted due to the word limits of the abstract required by Nature Communications.
3. Line 21: In the North Atlantic?
The offsetting effect on the OTEC power potential increase due to deep ocean warming is strongest in the North Atlantic Ocean (Supplementary Figure 6b). Although the offsetting effect in the South Atlantic Ocean is less evident than that in the North Atlantic Ocean, it is still stronger than that in the Pacific and Indian Oceans. In the revised manuscript, we have revised the sentence as: "The offsetting effect is more evident in the Atlantic Ocean than Pacific and Indian Oceans." (Line 17) 4. Line 23: The authors should remove the phrase starting with "unresolved by the majority of current generation of climate models" as those models parameterize the impact of eddies the eddies. The additional factor that was not directly examined was the impact of a weaker mean flow in the control climates in the CMIP6 that could explain the offset shows in Extended Data Figure 1. In addition, Extended Data Fig. 1 shows clearly that delta T is reduced by a similar amount in the CMIP6 runs as that in CESM-H. This figure suggests that the increase in OTEC potential may be well represented by the parameterized eddies in the CMIP6 models even if the mean OTEC is not.
(a) Reply to your comment on removing the phrase starting with "unresolved by the majority of the current generation of climate models" Thank you for pointing out this important issue. We have deleted this statement "unresolved by the majority of the current generation of climate models" in the revised manuscript.
(b) Reply to your comment on the effect of differed mean flows on the difference of simulated time-mean OTEC power potential between the CESM-H and coarseresolution CMIP6 CGCMs Griffies et al. (2015) compared the simulations between a high-resolution CGCM resolving mesoscale eddies and coarse-resolution CGCM parameterizing mesoscale eddies' effects using the GM90 parameterization (Gent & Mcwilliams, 1990). Similar to the finding of this study, they reported stronger thermal stratification in the highresolution than coarse-resolution CGCM and attributed this thermal stratification difference to the difference between the effects of resolved and parameterized mesoscale eddies. In the high-resolution (coarse-resolution) CGCM, the mean flows generate a downward vertical heat transport (VHT) that is largely balanced by the upward VHT by resolved (parameterized) mesoscale eddies. It indicates that mean flows act to cool the sea surface but warm the deep ocean, reducing the thermal stratification, i.e., a destratification effect. The opposite is true for mesoscale eddies, i.e., a restratification effect. However, the parameterized upward VHT in the coarseresolution CGCM is significantly weaker than the resolved VHT in the high-resolution CGCM (their Figure 12a and c). Accordingly, the downward VHT by mean flows also becomes weaker in the coarse-resolution CGCM than high-resolution CGCM to maintain an equilibrium state. As the destratification effect by mean flows is stronger in the high-resolution than coarse-resolution CGCM, mean flows cannot account for the enhanced time-mean thermal stratification in the CESM-H than coarse-resolution CMIP6 CGCMs. Instead, it is more likely to result from the stronger restratification effect by the resolved than parameterized mesoscale eddies.
The discrepancy between the VHT by resolved and parameterized mesoscale eddies suggests deficiencies of the GM90 parameterization widely used in the coarseresolution CGCMs. The deficiencies are likely to be multifaceted. In particular, the GM90 parameterization does not account for the VHT generated by mesoscale eddies via the turbulent thermal wind balance that is found to play an important role in the upper ocean (Jing et al., 2020). We have added the above discussion to the revised manuscript. Please see Line 238-251.

Line 30: Please give an example of what is meant by "intermittent renewable technologies
The phrase "intermittent renewable technologies" means renewable energy sources that cannot generate electricity steadily, such as wind and solar energy which relies on the availability of strong winds and sunlight. Table R1  The CP is defined as the ratio of actual electrical energy output over a given period to the theoretical maximum electrical energy output over that period and is often used to measure the steadiness of different energy sources. Among the common renewable energy sources, the OTEC has the highest value of CF and is thus most stable. In the revised manuscript, we have cited Garduño-Ruiz et al. (2021) and revised this phrase as: "Unlike many other renewable technologies based on intermittent energy sources such as winds and sunlight". (Line 25-26) We agree with you that the rate of strengthening of thermal stratification depends on the emission scenario. In the revised manuscript, we have deleted the phrase "with even a larger increasing rate" and revised the sentence as: "In the future, the strengthening of thermal stratification is likely to continue due to greenhouse warming, implying enriched OTEC resources." (Line 39-41) 8. Line 44: More explanation is needed here: do the authors think that contributions from ocean heat transport by the large scale flow is expected to change?
Yes, previous studies (Couldrey et al., 2021;Dias et al., 2020;Garuba & Klinger, 2016;Wu et al., 2012;Zika et al., 2021) suggest that the heat transport by oceanic flows changes significantly under greenhouse warming and plays an important role in determining the anthropogenic change of ocean thermal structure.
We have revised this part as: "On the one hand, the SST changes caused by local sea surface heat flux changes can be advected elsewhere by oceanic flows like a passive tracer, particularly into the deep ocean via the ventilation processes . On the other hand, changes in surface wind and buoyancy forcing under greenhouse warming drive changes in oceanic flows that redistribute the heat in the ocean and further affect the efficiency of ocean uptake of anthropogenic heat surplus via the redistribution feedback. 10. Line 48: I assume you men 1 degree (not 1 degree C).
11. Line 49: I assume the authors mean the coastal ocean here. That should be said explicitly.
We have replaced the phrase "nearshore region" with "coastal ocean" following your advice. Please see Line 56. 13. Line 63: This should read "potential power" not power as the study here gives an upper limit on what could be produced.
Thanks for your advice. It has been changed to "power potential" in Line 70-71 following your advice.
14. Line 75: Please replace "only about" with the mean and standard deviation. We are grateful to you for pointing out this issue. In the revised manuscript, we have added the standard error of OTEC power potential. The time-mean OTEC power potential in the EEZ is 4.87 ± 0.02 TW in the observation, significantly larger than 4.69  18. Line 105: I see good agreement with the increase of the CMIP6 within the standard deviation. This sentence should be modified to reflect that even though the mean delta T is small, the increase is in relatively good agreement. This also requires that the paragraph starting at line be modified. 19. Line 130 the statement starting with "Zoom" is not a sentence.
The sentence has been revised as:  25. In the figure captions "OTEC power" should be replaced with OTEC power potential. Revised.
26. Figure 3: the standard error of the trend estimates should be stated for each of the lines in the plots here.
The standard error has been added in Figure 3.
27. Line 262: Should be changed to "the ocean thermal stratification in practice" We have revised this part. Please see Line 340.
28. Line 263: how big is 5m/year compared to typical values of w from mixing or upwelling? Some context is needed. 5m/year seems like a larger number for the middepth ocean.
A cold-water intake rate wcw of 5m/year is on the same order of the large-scale vertical velocity in the mid-depth ocean interior estimated to be O(1 m/year) (Liang et al., 2017;Munk & Wunsch, 1998) but is more than an order of magnitude smaller than the wind-driven upwelling O(1 m/day) in the eastern boundary upwelling systems (Brady et al., 2017). We have added these reference values in the revised manuscript.

Line 274: Over what area would this hold? A few details of the sensitivity tests done
should be included.
The area here is the Atlantic OTEC region ( Supplementary Fig. 6b) (Line 200).
The CESM-H saves the entire diagnostic output for the temperature governing equation during 1920-1934. This allows us to test whether the horizontal mixing averaged over the Atlantic OTEC region is negligible compared to the other terms. Figure R3 shows the time series of individual terms in the OHC budget for the 800-1200 m water column over the Atlantic OTEC region. Both the time-mean value and variation of horizontal mixing are negligible compared to other terms in the budget, lending supports to our argument. In the revised manuscript, we have revised the sentence as: "The horizontal mixing by subgrid-scale processes is dropped, as its effect is negligible compared to other terms when averaged over a sufficiently large area considered here, i.e., the Atlantic OTEC region (Supplementary Fig. 6b; Supplementary Fig. 9)." (Line 370-373) Figure R3 | The time series of individual terms in the OHC budget for the 800-1200 m water column over the Atlantic OTEC region (Supplementary Fig. 6b). Here the OHC tendency (TD), heat transport convergence by mean flows Qmean, heat transport convergence by mesoscale eddies Qeddy, vertical mixing Q v mix and horizontal mixing Q h mix can be explicitly computed.

Reply to the second reviewer
We are very grateful to you for your time in carefully reading our manuscript and providing helpful comments that make our manuscript better. We have carefully considered each of your comments (in blue) and revised the manuscript accordingly.
Please find our response (in black) to your comments below.

Reviewer #2 (Remarks to the Author):
The paper studies the influence of global warming on the increase in power generation of OTEC plants. Such work is useful for extracting thermal energy from the ocean.
There are some concerns that the authors are encouraged to address.
1. The common range of temperature differences between the surface water and deep water in different regions of the world can be quantified in the paper. The thermocline in different regions and the reasons for differences in temperature difference with depth can be discussed to better explain the zonal differences in OTEC power. The steady power (Line 31) is mostly suitable for equatorial regions where the surface temperatures do not vary a lot with seasons. Large temperature differences mentioned in the abstract is also not very informative since OTEC operates on temperature differences of ~ 20°C.

(a) Reply to your comment on the distribution of temperature difference and underlying dynamics
Following your comment, we have displayed and discussed the spatial distributions of SST (Ts), the deep ocean temperature at 1000 m (T1000) and their difference (ΔT = Ts -T1000) as well as the underlying dynamics ( Fig. R1 and Supplementary Fig. 2). In the observation, the value of ∆T generally ranges from 0C to 25C in the global ocean, making the OTEC only available over approximately half of the global ocean. The spatial distributions of ∆T and OTEC power potential density Pnet are primarily attributed to that of the SST (Fig. R1a and c; Fig. 1b). As the SST decreases poleward due to the latitudinally varying solar radiation, a nonzero Pnet is confined to the low-latitude regions between 35S-40N. Furthermore, there is a notable zonal asymmetry in the Pnet. In the tropics, the SST and Pnet are higher in the Indo-Pacific warm pool than the Pacific and Atlantic equatorial cold tongues. The former is due to the accumulation of warm surface water by the wind-driven ocean circulations, whereas the latter is due to the upwelling of cold water from the thermocline into the surface layer (Talley et al., 2011a). In the subtropical oceans, high values of SST and Pnet are centered in the west of ocean basins caused by the winddriven anticyclonic ocean circulations (Talley et al., 2011a). The value of SST is further decreased in the eastern boundary upwelling systems due to the intense upwelling driven by along-shore equatorward winds (García-Reyes et al., 2015), leading to zero Pnet in these regions. The T1000 spatially varies to a less extent compared to the SST but plays a non-negligible role in the regional variability of ∆T and Pnet (Fig. 1b and c; Fig.   R1b). In particular, the injection of salty, warm Mediterranean Water into the deep Atlantic Ocean results in high value of T1000 in the eastern subtropical Atlantic Ocean (Richardson et al., 2000;Talley et al., 2011b), reducing the value of ∆T to below 20C and making Pnet become zero. Similarly, the relatively low values of ∆T and Pnet in the Arabian Sea than in the adjacent ocean are due to the injection of salty, warm Red Sea Water (Beal et al., 2000). Please see Line 95-113 in the revised manuscript for the above discussion. In this study, we focus on the long-term change of annual mean global OTEC power potential under greenhouse warming. As you pointed out, the OTEC power potential density Pnet at some locations can vary significantly at seasonal time scales.
Following your comment, we recompute the time mean and linear trend of OTEC power potential over the global ocean in different months, respectively (Table R1). The differences among months are not statistically different from each other. Therefore, the conclusion in Line 31 of our original manuscript is robust across all the seasons. This is likely because the seasonal variations in the northern and southern hemispheres largely cancel each other for the global OTEC power potential. 2. It would be interesting to see in the introduction some specific global warming mechanisms that target changes in ocean water temperatures, and by how much ocean water has changed over the years. Trends in changes of ocean surface and deep water temperatures over the years would be useful -higher rate of change in temperatures is projected in Extended Fig. 1. The high carbon emission scenario leading to temperature changes of ocean water discussed in the paper can also be quantified.
Thanks for your comment. We have briefly discussed the major mechanisms via which greenhouse warming causes temperature changes in the ocean. These  Fig. 6a). Both the sea surface and deep ocean exhibit significant warming under the high carbon emission scenario but the warming rate of the sea surface is much larger than that of the deep ocean.
3. It is easier to comprehend the influence of global warming on surface ocean water.
Deep cold water used by OTEC plants is ~1000 m below the ocean surface and the surface atmospheric effects would be almost negligible. Also, there is a lack in natural mixing between surface warm water and deep cold water. Hence, it is not easy to follow how DOW would be directly impacted by global warming. More discussions are required, particularly on the influence of ocean currents which is a focus of this paper.
DOW temperatures remain almost constant (4 -6 °C) at 1000 m throughout the world, while surface temperatures vary with region. Therefore, some form of evidence is necessary that the DOW does change with global warming.

(a) Reply to your comment on the mechanisms causing deep ocean temperature change under greenhouse warming
Thanks for your question. As you pointed out, turbulent mixing alone is inefficient to warm the deep ocean. There are two major mechanisms that can cause deep ocean temperature change under greenhouse warming. On the one hand, the SST changes caused by local sea surface heat flux changes can be advected elsewhere by oceanic flows like a passive tracer, particularly into the deep ocean via the ventilation processes . On the other hand, changes in surface wind and buoyancy forcing under greenhouse warming drive changes in oceanic flows that redistribute the heat throughout the ocean and further affect the efficiency of ocean uptake of anthropogenic heat surplus via the redistribution feedback . We have discussed these mechanisms in the revised manuscript. Please see Line 41-48.   6. The geographical differences between China and Mexico affects the OTEC power due to differences in vertical ocean thermal gradients. As mentioned above, reasons for such regional differences in thermal gradients and OTEC power should be well explained.
For the time-mean OTEC power potential (Fig. 1b), its difference between the SCS and GOM is primarily attributed to the difference in SST (Fig. R3). The SCS located at lower latitudes has higher SST than the GOM ( Fig. R3a and b), causing a larger temperature difference ΔT between the sea surface and deep ocean at 1000 m and thus a larger OTEC power potential.
As to the projected OTEC power potential change under greenhouse warming ( Fig.   2c and d), although both the SCS and GOM exhibit an evident increase in the OTEC power potential density Pnet by the end of this century, their spatial structures of Pnet changes differ substantially. The change in Pnet from 1992-2021 to 2071-2100 is relatively homogenous in the SCS, being 23 kW/km 2 or so. In contrast, the change of Pnet in the GOM is larger in the northern part (~40 kW/km 2 ), but decreases southeastward to ~15 kW/km 2 near the Yucatan Channel. This heterogeneous change of Pnet mimics that of SST change (Fig. R4). The depressed SST increase in the southeastern GOM is likely caused by the weakened Loop Current associated with a decline of Atlantic Meridional Overturning Circulation under greenhouse warming (Sen Gupta et al., 2021) that reduces the warm water intrusion into the GOM via the Yucatan Channel (Oey et al., 2013). Indeed, we find that the change of heat transport convergence by oceanic flows under greenhouse warming induces a strong cooling anomaly in the southeastern GOM (Fig. R5), contributing to the depressed SST increase there.
We have added the above discussion in the revised manuscript. Please see Line 164-176.  7. As acknowledged, the OTEC power depends on the thermal gradient with depth, regardless of the rates of changes in the surface and deep ocean water. Therefore, global warming may not always improve OTEC power, since the temperature gradient could change or remain same. This could be highlighted as a key outcome and could serve as a guide for potential future researchers investigating this topic. The growth of OTEC resource mentioned in the title may not be appropriate as well.
Thanks for your invaluable advice. Although the surface ocean warms faster than the deep ocean in terms of the global average (Cheng et al., 2017;Fox-Kemper et al., 2021), the local change of the difference between the sea surface and deep ocean temperature ΔT under greenhouse warming is controlled by complicated dynamics and can differ substantially from its global mean value. As shown in Fig. R6a, some highlatitude regions such as the subpolar North Atlantic Ocean do show a decreased ΔT under greenhouse warming. However, these regions are outside the OTEC region. In the OTEC region, there is a universal increase of ΔT under greenhouse warming (Fig.   R6a). Nevertheless, the change of ΔT can be locally much smaller than that caused by SST change alone ( Fig. R6a and b), suggesting the important role of deep ocean warming in retarding the ΔT increase under greenhouse warming. In the revised manuscript, we have highlighted this finding as a key outcome of the paper. Please see Line 228-232.
As the increase of ΔT under greenhouse warming holds in the OTEC region, we think the expression "the growth of OTEC resources under greenhouse warming" in the title is appropriate.